Question

example of word problems involving proportion, with solution​

Answer 1

Answer:

When solving proportion word problems, make sure it is set up correctly. Once you set up your proportion correctly, all you have to do if to replace values that you know and use an x or any other variable for the value you don't know. Let us solve the second proportion. ... Let us solve the second proportion.

1. Arrange the following ratios in descending order.

2 : 3, 3 : 4, 5 : 6, 1 : 5

Solution:

Given ratios are 2/3, 3/4, 5/6, 1/5

The L.C.M. of 3, 4, 6, 5 is 2 × 2 × 3 × 5 = 60

Now, 2/3 = (2 × 20)/(3 × 20) = 40/60

3/4 = (3 × 15)/(4 × 15) = 45/60

5/6 = (5 × 10)/(6 × 10) = 50/60

1/5 = (1 × 12)/(5 × 12) = 12/60

Clearly, 50/60 > 45/60 > 40/60 > 12/60

Therefore, 5/6 > 3/4 > 2/3 > 1/5

So, 5 : 6 > 3 : 4 > 2 : 3 > 1 : 5

2. Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.

Solution:

Sum of the terms of the ratio = 3 + 4 = 7

Sum of numbers = 63

Therefore, first number = 3/7 × 63 = 27

Second number = 4/7 × 63 = 36

Therefore, the two numbers are 27 and 36.

3. If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)

Solution:

x : y = 1 : 2 means x/y = 1/2

Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]

= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2

We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9

Therefore the value of (2x + 3y) : (x + 4y) = 8 : 9

4. A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.

Solution:

Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.

Then 2x × 50/100 + 3x × 25/100 + 4x × 20/100 = 510

x/1 + 3x/4 + 4x/5 = 510

(20x + 15x + 16x)/20 = 510

⇒ 51x/20 = 510

x = (510 × 20)/51

x = 200

2x = 2 × 200 = 400

3x = 3 × 200 = 600

4x = 4 × 200 = 800.

Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively.

Answer 2

Answer:

• Example
• A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d.